King Charles III and Queen Camilla are set for a pomp-filled trip to the Big Apple Wednesday — but locals suggested a different itinerary if the royal couple wants to see the so-called real New York. The UK monarch and his wife have a jam-packed schedule for their daylong tour of Manhattan that includes paying their respects at the 9/11 Memorial & Museum with Mayor Zohran Mamdani and stopping by the New York Public Library. Britain’s head of state hasn’t hopped across the pond to New York since Charles’ late mother Queen Elizabeth II toured in 2010. Charles, who became king in 2022 at 73, was last in the city in 2007, when he and Camilla visited to the Promise Academy charter school in Harlem. But some New Yorkers in the outer boroughs questioned why the couple — who are stopping by during their state visit to Washington DC — were only sticking to Manhattan. King Charles will visit the Big Apple Wednesday for the first time since 2007.…